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29 3 0 Show 38 CHAPTER 2. 6 (Short-run demand and supply) (a) Where output is at the optimal level for the …xed input, short-run and long-run total costs are equal. (b) At this output level, short- and long-run marginal costs are equal. (c) At this output level, short- and long-run input demands are equal. (d) The short-run marginal cost curve is at least as steep as the long-run marginal cost curve. (e) Long-run input demands are at least as elastic as short-run demands. 16 illustrates these results in the case where long-run marginal costs are rising.

We shall develop this point later, but for the moment, let us set it aside and return to the overall optimisation problem of the …rm. 4 Assembling the solution Let us now see what we get when we put together the solutions to the two component problems, cost-minimisation and output optimisation. The main result is as follows: 1 7 We have ruled out < 0, but what would be likely to happen in a market if See page 57. 1 8 What must be true about the production function for such a q to exist? > 0? 3.

4 illustrates the case of homothetic contours: each isoquant appears like a photocopied 4 Show that ij = ji . You may …nd the material on page 496 useful. 16 CHAPTER 2. THE FIRM enlargement; along any ray through the origin all the tangents have the same slope so that the MRTS depends only on the relative proportions of the inputs used in the production process. 7) where r is a positive scalar. 7) then it is said to be homogeneous of degree r. Clearly the parameter r carries important information about the way output responds to a proportionate change in all inputs together: if r > 1, for example then doubling more inputs will more than double output.